Question

Calculate the average rate of change over the interval [1, 5] for the following function. H(x)=-2x^2-3x-1

Answer 1

`Rate = -15`

Explanation:

Given

`H(x) = -2x^2 - 3x - 1`

`[a,b] = [1,5]`

Required

The average rate of change

This is calculated using:

`Rate = (H(b) - H(a))/(b - a)`

Substitute values for a and b

`Rate = (H(5) - H(1))/(5 - 1)`

`Rate = (H(5) - H(1))/(4)`

Solve for H(5) and H(1)

`H(5) = -2*5^2 - 3*5 - 1 = -66`

`H(1) = -2*1^2 - 3*1 - 1 = -6`

So, the expression becomes:

`Rate = (-66 - (-6))/(4)`

`Rate = (-66 + 6)/(4)`

`Rate = (-60)/(4)`

`Rate = -15`